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We obtain a solution of the quasilinear equation Ã¢ÂˆÂ’ÃŽÂ”pu=f(u) in ÃŽÂ©, u=0, on Ã¢ÂˆÂ‚ÃŽÂ©. Here  the nonlinearity f is superlinear at zero, and it is located near infinity between two functions that belong to a class of functions where the Ambrosetti-Rabinowitz condition is satisfied. More precisely, we consider the class of functions that are asymptotically homogeneous of index q

Superlinear Equations Involving Nonlinearities Limited by Asymptotically Homogeneous Functions